I am thinking of building two of tapped horn subwoofers to go with my Sound Lab electrostatic speakers. I know tapped horn subwoofer has high output and they are high efficient. But, do tapped horns have low distortion? Are tapped horn subwoofers fast?

Bass can't sound "fast" or "slow". All sound (for a given location - humidity and pressure will alter it) travels at ~340m/s. Compared to other designs, impulse response isn't usually a strong point.

A decent TH will have low distortion, but, as always, the driver choice plays a large role in this. I can say this: as THs reduce excursion (above the lower cutoff) over a sealed design eq'd to the same output. Following this, distortion should be lower than a driver that's moving further to keep up.
They have a bandwidth of 2 octaves. Take a quarter of your chosen upper cutoff, and the best extension you'll get is that frequency. Usually. That's a general rule of thumb. You might get a few Hz extra, you might miss out on a few Hz.

To see if they're worth while, try a reasonably cheap build. The THs linked in my signature are very good. Certainly better than the sealed 2x8" drivers they replaced. Given sufficient power, they'll fill a large room down to frequencies that you wouldn't expect from such a small driver.
A day's work should get a pair made. Have you much experience building cabinets?

I am thinking of building two of tapped horn subwoofers to go with my Sound Lab electrostatic speakers. I know tapped horn subwoofer has high output and they are high efficient. But, do tapped horns have low distortion? Are tapped horn subwoofers fast?

Your comments and suggestions are greatly appreciated.

Tapped horns (TH) can increase level by six dB (more or less) over ported cabinets (BR). When compared to the regular cabinet at the same SPL level, distortion is reduced.

When compared at the same power level, distortion is higher in the TH compared to BR.

“Fast” is a subjective term, different cabinet designs using different drivers all have different phase and frequency response, characterizing an entire category of speakers is impossible, examples that sound “slow” can be found in any category of speaker design.

That said, in terms of “punch” (“fast”) , phase or transient accuracy, I’d put the continuum in this order, best to worst:

1) Horn loaded using a compression chamber
2) Sealed or infinite baffle
3) Tapped Horn
4) Sealed using a passive radiator
5) BR
6) Bandpass (output of one BR system feeding a second chamber using another port)

Although I have thus far not heard anything from category #6 I have cared for, I have heard systems in the first five that all sound “fast”, that is low drums, upright bass, etc. sound quite similar to the recorded counterpart.

Many of the objective and subjective differences are discussed in these posts:

I had been using various ported designs in my subwoofers for years before I decided to get a little help designing a TQWT. I'll never look back. Using the same drivers that I had previously in a BR box, I've got more sensitivity, better extension and a feeling of "ease" - not sure if I'm using that term right, but that's how it seems to me.

Especially at low levels, which is what amazed me most, I think, where before I would have to have the volume pretty juiced up to start hearing lower notes, now even at "everyone else in the house is asleep" levels, I can still hear things like the almost infrasonic hum that the starship Enterprise produces.

I had been using various ported designs in my subwoofers for years before I decided to get a little help designing a TQWT. I'll never look back. Using the same drivers that I had previously in a BR box, I've got more sensitivity, better extension and a feeling of "ease" - not sure if I'm using that term right, but that's how it seems to me.

Especially at low levels, which is what amazed me most, I think, where before I would have to have the volume pretty juiced up to start hearing lower notes, now even at "everyone else in the house is asleep" levels, I can still hear things like the almost infrasonic hum that the starship Enterprise produces.

Just my opinion

A six dB increase means only 1/4 the power is needed to achieve the same level.

Conventional means can be used instead of "warp drive" when power demands are reduced by 1/4 .

Back to the subjective term of “speed”, phase alignment at crossover is necessary for a system to sound “tight” or “fast” around the crossover frequency, long horns, TH, TQWT may need the tops delayed to “get it right”.

Without digital delay, by luck or design, a horn, TH, TQWT sub may be one (or more) wavelength behind the top (“slow” sounding) but still be “in phase” at the acoustical crossover.

Although you "may never look back" at your various ported designs, you may want to look forward to adding a DDL to your tops if you want "ease" and "punch", phase accuracy rather than just phase alignment.

Although you "may never look back" at your various ported designs, you may want to look forward to adding a DDL to your tops if you want "ease" and "punch", phase accuracy rather than just phase alignment.

Just my opinion .

Art Welter

I'd love to mess with stuff like that, but at the moment, all my speakers are passive. Just a handful of crossover parts separate my subs from mains

I've been considering a multichannel amplifier and using a MiniDSP...which I gather can do the delay as well as the crossovers, but unfortunately finances won't allow for that just now.

With passive components you may find moving your subs around a wavelength (at the acoustical crossover) closer to your listening position may improve the sound.

You may gain a lot more sub level due to the inverse square law, too, which may require padding the tops. If you had the subs in a corner to start with, level may end up being about the same.

That's an awesome idea, and I might just have enough room to try it.

You know, now that you mention it, I noticed that my left sub seems to mate better with my left main better, I thought that I had a bad capacitor in the right, but now that you mention this, it dawned on me that my left sub in the left corner is about 4 meters (xo is 80 hz about 4.3 meters) further away from my listening position than the right one!

I learn something new around here every day.

Edit: I can't tell left from right today, but I understand nonetheless and I'll be spending some time fiddling with everything this weekend for sure.

You know, now that you mention it, I noticed that my left sub seems to mate better with my left main better, I thought that I had a bad capacitor in the right, but now that you mention this, it dawned on me that my left sub in the left corner is about 4 meters (xo is 80 hz about 4.3 meters) further away from my listening position than the right one!

I learn something new around here every day.

Edit: I can't tell left from right today, but I understand nonetheless and I'll be spending some time fiddling with everything this weekend for sure.

Sounds like a pretty large room. If you can move both the subs another 4.3 meters (or so, depending on path length of the TQWP) closer to the listening position than the mains you may find an improvement in alignment over just taking care of the time alignment issues between L and R sub you have presently.

Or not.

Room modes are hard to predict, and can easily trump the subtleties of LF phase and time alignment. I'd rather listen to a bad sub in a good room over a good sub in a bad room...

Sounds like a pretty large room. If you can move both the subs another 4.3 meters (or so, depending on path length of the TQWP) closer to the listening position than the mains you may find an improvement in alignment over just taking care of the time alignment issues between L and R sub you have presently.

Or not.

Room modes are hard to predict, and can easily trump the subtleties of LF phase and time alignment. I'd rather listen to a bad sub in a good room over a good sub in a bad room...

Yeah, it's a little bizarre in here because of the way it's laid out, I only have 2 corners to wedge the subs into. The front door is in the back corner on one side and the entrance for the kitchen on the other. The listening area is along the long wall, but not in the center, because the couch would block the stairs going up if it was also in the center :P The room is approximately 4m by 6.5m.